Functions Contents - G
Integral calculus
The definite and indefinite integrals
The area between the graph of a function and the x-axis over a closed interval
Geometric interpretation of the definite integral
Properties of the definite integral
The definite integral over interval of zero length
Reverse order of integration
The constant multiple rule
The integral of the sum or difference of two functions
Internal addition of the definite integral
The definite integral of an odd function
The definite integral of an even function
The definite integral of a nonnegative and nonpositive functions
Relationship of the definite integrals of two functions over the same interval of integration
Absolute integrability
The mean value theorem
The average value of a function over the given interval
The indefinite integral
Integration - inverse of differentiation
Constant of integration, the arbitrary constant term in the expression of the indefinite integral
Evaluating the indefinite integral example
The fundamental theorem of calculus
The fundamental theorem of differential calculus
Evaluating definite integrals using indefinite integrals
The fundamental theorem of integral calculus
Evaluating the definite integral examples
The indefinite integral
Basic rules of integration
Table of indefinite integrals
The indefinite integral applications
Kinetic equation of free fall
Exponential growth and decay (increase and decrease)
Evaluation of indefinite integrals using some basic integration rules and formulas examples
Use of basic integration rules and formulas to solve indefinite integrals
Substitution rule
Evaluating the indefinite integrals using substitution rule examples
Evaluating the indefinite integrals using substitution rule solutions
Use of the substitution rule to solve indefinite integrals examples
Indefinite integrals of irrational functions
Integration by parts rule
Evaluating the indefinite integrals using the integration by parts formula examples
Evaluating the indefinite integrals using the integration by parts formula solutions
The indefinite integrals containing quadratic polynomial (trinomial)
The indefinite integrals containing quadratic polynomial examples
Recursion formulas - use of
integration by parts formula
Recursion formulas - use of
integration by parts formula examples
Substitution and definite integration
Substitution and definite integration examples
Integrations by parts and the definite integral
The improper integrals
The improper integral definition
The improper integrals examples
Differentiation and the integration of infinite series
Differentiation and integration of infinite series examples
Applications of the definite integral
The area of a region in the plane
The area between the graph of a curve and the coordinate axis
The area between the graph of a curve and the coordinate axis examples
The area bounded by a parametric curve
The area of the sector of a curve in polar coordinates
The area of the sector of a curve given in Cartesian (or rectangular) coordinates
The area of the sector of a parametric curve
The area between two curves
The area between two curves examples
Length of plane curve, arc length
Arc length of a parametric curve
Arc length of a curve in polar coordinates
The volume of a solid of revolution
The volume of a sphere
The volume of a spherical segment
The volume of a cone
The surface area of a solid of revolution
The lateral surface area of a cone
The surface area of a spherical cap
The surface area of an ellipsoid
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